Heat oven to 400 degrees F. Place the sweet potatoes, parsnips, thyme, and garlic in a medium saucepan. Cover with cold water and bring to a boil. Reduce heat and simmer, covered, until the vegetables are tender, 15 to 18 minutes. Discard the thyme. Reserve 1/4 cup of the cooking water, drain the vegetables, and return them to the pot. Mash with the yogurt and 1/4 teaspoon pepper (adding the reserved cooking water, 1 tablespoon at a time, if the mixture seems dry).

Meanwhile, in a small bowl, whisk together the vinegar, jam, and mustard. Heat the oil in a large skillet over medium-high heat. Season the pork with 1/4 teaspoon each salt and pepper and cook, turning occasionally, until browned on all sides, 4 to 5 minutes total. Transfer to a rimmed baking sheet and roast until the internal temperature reaches 145 degrees F, 12 to 15 minutes. Transfer to a cutting board and let rest for 5 minutes before slicing.

Add the vinegar mixture to the skillet. Return to medium-low heat and cook, whisking until the jam melts and the mixture is syrupy, about 1 minute. Serve with the pork and the vegetable mash.

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